TUTLTLLLL Roll No. Totat No. of Pages: 03 Total No. of Questions 18

B.Tech. (CSE/IT) (2018 & Onwards) (Sem.-2) MATHEMATICS-I

Subject Code BTAM-204-18 M.Code: 76257

Time 3 Hrs. Max. Marks : 60

INSTRUCTIONS TO CANDIDATES 1. SECTION-A is COMPULSORY cons isting of TEN questions carrying TWO marks

each. 2. SECTION - B& C have FOUR questions each.

Attempt any FIVE questions from SECTION B &C carrying EIGHT marks each. 3.

4. Select atleast TWO questions from SECTION B & C.

SECTION-A

Answer the following:

1) Define Probability of an event.

2) Let X be the random variable such that P(X = -2) = P (X=-1), P(X =2) = P(X=1) and P(X>0)= P(X<0) = P(X = 0). Obtain the probability mass function of X.

3) What is Spearman's rank correlation coefficient?

4) State chi-square and Student's t- distributions.

5) Define Discrete Variables.

If arithmetic mean is 56.50, median is 59.50 and standard deviation is 12.40. Find the 6) skewness.

7) Differentiate between the discrete and continuous random variables.

8) Write the normal equations for the curve fitting y =a + bx by the method of least squares.

9) Define Regression Coefficients.

10) Define Null and alternative hypothesis.

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SECTION-B

11) a) Find the Karl Pearson's coefficient of skewness from the following data

Size 3 Frequency: 10 18 30 25 12 2

b) Show that the corelation coefficient ry between the two variables x and y is given

by

Ty 20y

where o oy and oy are the standard deviations ofx, y and x- y respectively.

12) a) Two fair dice are thrown independently. Three events A, B and C is defined as follows

A: Even face with first dice.

B:Even face with second dice.

C: Sum of the points on the two dice is odd.

Discuss the independence of events A, B and C.

b) From a bag containing 4 white and 6 red balls, three balls are drawn at random. If each white ball drawn carries a reward of Rs. 4 and each red ball Rs. 6, find the

expected reward of the draw.

13) a) With the usual notations, find p for a binomial random variable X if n = 6 and

9 P(X =4)= P(X = 2).

b) If the flowers on a truck are classified as A, B, and C according to a size-weight index as: under 75, between 75 and 80, and above 80. Find approOximately (assuming a

nomal distribution) the mean and standard deviation of a lot in which A are 58%, B are 38% and C are 4%. Given that P(0< Z< 020) = 0.08 and P(0<Z< 1.75) = 0.46,

where Z is standard nomal variate.

14) From the given data, find

Marks in Mathematics 25 38 35 3231 36 29 38 34 32 Marks in Statistics 43 46 49 41 36 32 31 30 33 39

a) The two regression equations,

b) The cocfficient of correlation between the marks in Mathematics & Statistics

c) The most likely marks in Statistics when the marks in Mathematics are 30.

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SECTION-C

15) The intelligence quotients (10) of 16 students from B.Tech. Ind year showed a mean of 107 and a standard deviation of 10, while the IQs of 14 students from B.Tech. 1st year showed a mean of 112 and a standard deviation of 8. Is there a significant difference between the 1Qs of the two groups at significance levels of 0.05? Given that critical value at 28 degree of freedom with 5% level of significance is 205.

16) a) Suppose that the life length of the two bulbs Bl and B2 have distribution N(x, 40,36) and N(x; 45, 9) respectively. If the bulb is to be used for 45-hour period, which bulb is to be preferred? If it is to be used for 48-hour period, which bulb is to be preferred? Given that P(Z<0.83)=0.7967, P(Z<1.33)=0.9082, P(Z<1.00) = 0.8143.

b) The time required to repair a machine is exponentially distributed with parameter % What is the probability that a repair time exceeds 2 hours? What is the conditional probability that a repair time takes at least 10 hours given that its duration exceeds 9 hours?

17) The prices of a commodity during 2011-2016 are given below. Fit a parabola Y =a+bX + cX to these data.

2013 2014 2014 2015 2016

192 Year (XX 2011 2012

Price (Rs.)Y L 100 107 128 140 181

18) a) Before an increase in excise duty on tea, 400 people out of a sample of 500 persons were found to be tea drinkers. After an increase in duty, 400 peoples were tea drinker in a sample of 600 people. Using standard error of proportion, state whether there is a

level of significance at 5%. significant decrease in the consumption of tea. Tak

b) The number of scooter accidents per month in a certain town were as follows

12820 214 10156 94 Are these frequencies in agreement with the belief that accident conditions were the same

during this 10 month period? (The table value of ? for 9 d.f at 5% level of significance is 16.919).

NOTE: Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

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